Is there any way to keyframe values within a SimpleDeform modifier?
You can like most other fields in blender. You just need to remember the shortcut i while hovering over the field or simply right-click (on the field) > Add keyframe. The field's color is yellow when a keyframe is set to the current frame, and green when at least one keyframe is set to another frame. Remember to change the current frame in the timeline when you change keyframes.